Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Is a cousin of"
A)Transitive; not an equivalence relation
B)Symmetric and transitive; not an equivalence relation
C)Symmetric; not an equivalence relation
D)None; not an equivalence relation

Question

Quizplus · Accepted Answer

The relation "is a cousin of" is symmetric because if person A is a cousin of person B, then person B is also a cousin of person A. However, it is not reflexive because a person is not a cousin of themselves, and it is not transitive because if person A is a cousin of person B, and person B is a cousin of person C, it does not necessarily mean that person A is a cousin of person C. Therefore, it is not an equivalence relation.

Tell Whether the Relation Is Reflexive, Symmetric, or Transitive on the Set